Read it again any time, including while you work through the exercises.
Here is a remarkable fact about multiplication: if a product equals 0, then at least one of its factors is 0. It cannot be otherwise! Try multiplying two nonzero numbers: 2 × 3, (-5) × 4, 0.1 × 0.1... you will never get 0. Zero does not appear out of thin air: it was already in the product.
This property becomes an equation-solving machine. Facing (x - 3)(x + 7) = 0, no need to expand: the product is zero, so x - 3 = 0 or x + 7 = 0. Two easy mini-equations instead of one big one: x = 3 or x = -7. The equation has TWO solutions, and that is new: until now, your equations had only one.
The important word is OR: it is enough for ONE factor to vanish for the product to be zero. When x = 3, the first factor is 0 and the second is 10: the product is indeed 0 × 10 = 0. Both factors do not need to vanish at the same time.
Often the equation does not arrive in product form: x² = 9x, for instance. The vital reflex: bring everything to zero on one side (x² - 9x = 0), then FACTOR (x(x - 9) = 0) to recover a product equation. Above all, never divide both sides by x: you would silently lose the solution x = 0.
This technique is a key gateway in algebra: it is what will later let you solve equations of degree 2 and beyond. Zero product, zero factor: engrave that sentence in your memory.